Points , and are the midpoints of the sides of triangle . Find the coordinates of the points , and . (Labels , and are arbitrarily assigned to coordinates).Source: NCTM Mathematics Teacher 2008

SOLUTION
Draw a first line passing through and parallel to . Equation of the first line
Slope of
Draw a second line passing through point Z and parallel to . Equation of the second line
Substitute the values of into the equation
Equation of the second line
The two lines intersect at point the coordinates of which satisfy both Eq. and .
Solving for yields
Coordinates of vertex .
Suppose is the midpoint of side . The midpoint formula yields the coordinates of vertex
Coordinates of vertex .
Similarly is the midpoint of side . In this case the midpoint formula yields the coordinates of
Coordinates of vertex .